We introduce a model based on Ordinary Differential Equations to describe how two mutually exclusive groups progress through the organization hierarchy. The intended application of the model is to gender imbalance at the Professorial level in European Universities, however, the model is entirely generic and may be applied in other contexts also. The model can be applied at the organizational level but equally at the sectoral level, meaning it has implications for Social Science. Previous research on gender imbalance in European universities has focused on large-scale statistical studies. Our model represents a point of departure, as it is deterministic (i.e. based on Ordinary Differential Equations). However, the model contains unknown parameters, which can be estimated from the prior statistical literature. We introduce a glass-ceiling index g to characterize an imbalance at the top of the organizational hierarchy (g ≠ 1 indicates imbalance). Our model can be used to pinpoint the proximate cause of any such balance in the long-time steady-state value of g. Specifically, the steady-state value of g is a function of the ratio of the progression rates of the different groups through the hierarchy. Accordingly, while the difference between the two progression rates may be small in percentage terms, what matters for the long-time structure of the hierarchy is the ratio, which in practice may be large (our analysis makes these terms precise). As our model is dynamic, we can also estimate how long it takes to reach steady state – the limiting factor here is twofold, and depends on the retirement rate at the upper (managerial / professorial) level, but also, the growth rate of the organization's headcount.